The document summarizes research from the Congressional Budget Office on inflation and the Phillips curve. It finds that while the aggregate Phillips curve is quite flat, estimating the relationship at the component level reveals differences between goods and services inflation. Services inflation remains procyclical, driven by domestic factors, while goods inflation has become less procyclical in recent decades due to globalization and other structural forces. The document also examines how measures of inflation expectations have evolved from being backward-looking to becoming more anchored, though consumers' expectations remain more responsive to shocks than professionals' forecasts.

1. Congressional Budget Office
66th Annual Economic Outlook Conference
Research Seminar in Quantitative Economics, University of Michigan
November 15, 2018
Yiqun Gloria Chen
Macroeconomic Analysis Division
Inflation and the Phillips Curve
As developmental work for analysis for the Congress, the information in this presentation is preliminary and is being circulated to stimulate discussion and critical comment.

2. 1
CBO
Inflation: 1948–2018

3. 2
CBO
Inflation Expectations: 1948–2018

4. 3
CBO
Unemployment: 1948–2018

5. 4
CBO
This flow chart shows the structure of CBO’s inflation model for the PCEPI, as well as the spending shares for its components. Those components include PCNFOOD: Food &
Beverage Purchases for Off-Premises Consumption; PCNENERGY: Gasoline & Other Energy Goods; PCSENERGY: Electricity and Gas; PCDELEC: Video, Audio, Photo & Info
Processing Equipment & Media; PCDMVAP: Motor Vehicles & Parts; PCDMED: Therapeutic Appliances & Equipment; PCDOTH: Other Durable Goods (CBO’s calculation);
PCNMED: Pharmaceutical & Other Medical Products; PCNOTH: Other Nondurable Goods (CBO’s calculation); PCSHOUS: Housing; PCSMED: Health Care Services; and PCSOTH:
Other Services (CBO’s calculation).
Structure of CBO’s Model for the Personal Consumption
Expenditures (PCE) Price Index

6. 5
CBO
𝜋𝜋𝑡𝑡= 𝐸𝐸𝑡𝑡 𝜋𝜋𝑡𝑡+1 − 𝜷𝜷 𝑈𝑈𝑡𝑡 − 𝑈𝑈∗
+ 𝛾𝛾𝑍𝑍𝑡𝑡 + 𝜖𝜖𝑡𝑡
 Determinants of inflation
– 𝐸𝐸𝑡𝑡 𝜋𝜋𝑡𝑡+1: Inflation expectations
– 𝛽𝛽 𝑈𝑈𝑡𝑡 − 𝑈𝑈∗
: Unemployment gap, or other measures of slack in the economy
– 𝛾𝛾𝑍𝑍𝑡𝑡: Supply-side shocks (for example, relative price of imports, energy, etc.)
 Issue 1: Cyclical sensitivity of inflation
– For the price index of personal consumption expenditures (PCEPI) excluding food
and energy (“XFE” or “core-XFE”): 𝛽𝛽 has declined from 0.3~0.4 in the 1970s to
0.05~0.1 in the most recent decades.
– Does inflation still respond to slack?
 Issue 2: The form of inflation expectations
– “Accelerationist”: 𝐸𝐸𝑡𝑡 𝜋𝜋𝑡𝑡+1= 𝐴𝐴 𝐿𝐿 𝜋𝜋𝑡𝑡−1 (distributed lags of inflation)
– “Anchored”: 𝐸𝐸𝑡𝑡 𝜋𝜋𝑡𝑡+1= 𝜋𝜋∗
(constant)
– Combined: 𝐸𝐸𝑡𝑡 𝜋𝜋𝑡𝑡+1=𝜶𝜶𝐴𝐴(𝐿𝐿)𝜋𝜋𝑡𝑡−1 + (𝟏𝟏 − 𝜶𝜶)𝜋𝜋∗
Expectation-Augmented Phillips Curve

7. 6
CBO
Cyclical Sensitivity of Inflation:
Goods Versus Services

8. 7
CBO
 Goal: Understanding why the aggregate Phillips curve is so flat
 Method: Estimating Phillips curve equations at the component level
– Measure of slack: The unemployment gap (CBO’s estimate)
– Sample: 1998Q1–2018Q3 (stable inflation expectations)
– Control for: Relative price of imports and energy goods, outliers (for example, “cash
for clunkers”)
– Similar to: Stock and Watson (2018); Struyven (2017)
 Main Finding: Divergence between goods and services in terms of cyclical
sensitivity
– Services: Remained largely pro-cyclical—for example, shelter
– Goods: Not pro-cyclical in the past two decades
 Dampening the slope of the aggregate Phillips curve
 Exception: Food prices
Phillips Curve Model at the Component Level

9. 8
CBO
Shelter Inflation

10. 9
CBO
Auto Inflation

11. 10
CBO
Services: Largely Pro-Cyclical
Unemployment
Gap
Lagged
Inflation
Constant Adjusted R2
PCE: Services Less Energy -0.14 0.32 1.91 0.46
(0.00) (0.01) (0.35)
PCE: Housing Services -0.23 0.58 1.29 0.80
(0.00) (0.00) (0.24)
CPI-U: Owner's Equivalent of Rent -0.21 0.62 1.13 0.78
(0.00) (0.00) (0.24)
CPI-U: Rent of Primary Residence -0.15 0.67 1.16 0.84
(0.00) (0.00) (0.26)
PCE: Health Care Services -0.06 0.62 0.92 0.42
(0.38) (0.00) (0.26)
PCE: Services Less Energy, Rent of Shelter & Health care -0.04 0.35 1.72 0.38
(0.50) (0.00) (0.28)
CPI-U: Services Less Energy Services & Rent of Shelter -0.15 0.40 1.88 0.34
(0.01) (0.00) (0.40)
CPI-U: Medical Care Services -0.05 0.70 1.15 0.34
(0.51) (0.00) (0.45)
CPI-U: Food away from Home -0.09 0.62 1.05 0.57
(0.05) (0.00) (0.25)
CPI-U: Education Services -0.07 0.93 0.30 0.81
(0.16) (0.00) (0.29)
CPI-U: Transportation Services -0.02 -0.11 3.20 0.16
(0.87) (0.27) (0.36)

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CBO
Goods: Largely Not Pro-Cyclical, Except Food
Unemployment
Gap
Lagged
Inflation
Constant Adjusted R2
PCE: Durable Goods 0.08 0.28 -1.54 0.27
(0.31) (0.01) (0.24)
PCE: Motor Vehicles and Parts 0.31 0.30 -0.21 0.43
(0.05) (0.00) (0.25)
PCE: Video, Audio, Photo & 0.16 0.60 -3.95 0.44
Information Processing Equipment & Media (0.34) (0.00) (0.87)
PCE: Other Durable Goods (including Medical Equipments) -0.10 0.38 -0.50 0.27
(0.28) (0.00) (0.19)
PCE: Nondurable Goods Less Energy -0.14 0.73 0.39 0.44
(0.05) (0.00) (0.17)
PCE: Food & Beverage Purchased for Off-Premises Consumpt -0.24 0.66 0.71 0.55
(0.04) (0.00) (0.24)
CPI-U: Food at Home -0.27 0.63 0.82 0.52
(0.05) (0.00) (0.28)
CPI-U: Alcoholic Beverages -0.17 0.34 1.47 0.16
(0.04) (0.00) (0.26)
PCE: Pharmaceutical & Other Medical Products -0.02 0.33 2.02 0.20
(0.88) (0.00) (0.39)
PCE: Other Nondurable Goods 0.08 0.25 0.00 0.42
(0.46) (0.01) (0.18)
CPI-U: Apparel 0.54 0.14 -0.69 0.22
(0.00) (0.18) (0.30)

13. 12
CBO
 Services
– Prices are largely determined by domestic and/or local factors
 Household maintenance, restaurants, etc.
– Cannot be inventoried
 Goods
– Lots of measurement issues and noise from one-off price shocks (Stock and
Watson, 2018)
 Measurement issue very severe for apparel, recreational goods, financial
services, etc.
 One-off price shocks: “cash for clunkers” (2009), federal tobacco tax hike
(2009)
– Tend to be more heavily influenced by long-run structural forces
 Globalization: Abdih et al. (2016) and others
 “The Amazon effect”: Goolsbee and Klenow (2018)
 Increasing industrial concentration?
Goods Versus Services: Possible Explanations

14. 13
CBO
 Services Components
– Generally, Phillips curve equations at the component level work relatively well
– Special case: PCE health care services (policy plays a large role)
 CBO’s model incorporates CBO’s projection of Medicare reimbursement rate
growth
 Goods Components
– “Top-down Approach”: CBO currently uses core PCE inflation (from the
aggregate Phillips curve) as an input in the equations for goods components
 Keep track of movements in relative prices
 Judgment in sector-specific trends
 Control for relative price of imports, one-off price shocks, etc.
Forecasting Inflation at the Component Level

15. 14
CBO
Modeling Inflation Expectations:
Backward-Looking Versus Anchored

16. 15
CBO
 Reduced-form:
𝜋𝜋𝑡𝑡= 𝜶𝜶𝐴𝐴(𝐿𝐿)𝜋𝜋𝑡𝑡−1 + (𝟏𝟏 − 𝜶𝜶)𝜋𝜋∗ − 𝛽𝛽 𝑈𝑈𝑡𝑡 − 𝑈𝑈𝑡𝑡
∗
+ 𝛾𝛾𝑍𝑍𝑡𝑡 + 𝜖𝜖𝑡𝑡
o 𝐴𝐴(𝐿𝐿)𝜋𝜋𝑡𝑡−1: Use four lags of past inflation
o 𝜋𝜋∗
: Long-run inflation/“anchor”
o 𝑈𝑈𝑡𝑡 − 𝑈𝑈𝑡𝑡
∗
: The unemployment gap (CBO’s estimate)
o 𝑍𝑍𝑡𝑡: Supply-side shocks, including relative prices of imports and energy goods
o Sample: 1998Q1–2018Q3
 Blanchard (2016): “The Phillips Curve: Back to the ’60s?”
– Shows 𝜶𝜶 declined over time and is currently very small for headline CPI.
 But component-level analysis implies that the measure of inflation matters
 This exercise: Try ten different measures of aggregate inflation
Estimating the Aggregate Phillips Curve

17. 16
CBO
 Three measures of headline inflation
– Headline CPI-U (BLS) and Headline PCEPI (BEA)
– Chained CPI-U (BLS)
Ten Measures of Inflation

18. 17
CBO
 Seven measures of core inflation
– Approach 1: Remove the most volatile price changes
 XFE CPI-U (BLS) and XFE PCEPI (BEA)
 Median CPI-U and 16%-Trimmed-Mean CPI-U (Federal Reserve Bank of
Cleveland)
 Rank price changes by size each month, and trim the items with price
changes that are above or below a certain threshold
 “Median” is just extreme trimming
 Trimmed-Mean PCEPI (Federal Reserve Bank of Dallas)
 Trimming point chosen optimally every month
– Approach 2: Remove the most frequent price changes
 Sticky CPI-U and Sticky-XFE CPI (Federal Reserve Bank of Atlanta)
 Price changes every 4.3 months or longer (Bils and Klenow, 2004)
Ten Measures of Inflation (Continued)

19. 18
CBO
Seven Measures of Core Inflation

20. 19
CBO
 Relative weight of lagged inflation and constant/“anchor”:
– Overall inflation: 𝛼𝛼 ≈ 0.2, consistent with Blanchard (2016) for headline CPI
Estimation Results: I
This figure plots the sum of the estimated coefficients on lagged inflation terms using recursive samples that start in 1998Q1 and end in 2012Q1, 2012Q2, …, and 2018Q1. The
Phillips curve equations are “unrestricted,” as no assumption was imposed on the value of π* before the estimation. Instead, the intercept of the equation, which, in theory, equals απ*,
was estimated and then the values of α and π* were calculated by assuming the long-run restriction on the estimated coefficients.

21. 20
CBO
 Relative weight of lagged inflation and constant/“anchor”:
– Overall inflation: 𝛼𝛼 ≈ 0.2, consistent with Blanchard (2016) for headline CPI
– Core inflation: 𝛼𝛼 ≈ 0.5, particularly for non-XFE measures.
Estimation Results: I (Continued)
This figure plots the sum of the estimated coefficients on lagged inflation terms using recursive samples that start in 1998Q1 and end in 2012Q1, 2012Q2, …, and 2018Q1. The
Phillips curve equations are “unrestricted,” as no assumption was imposed on the value of π* before the estimation. Instead, the intercept of the equation, which, in theory, equals απ*,
was estimated and then the values of α and π* were calculated by assuming the long-run restriction on the estimated coefficients.

22. 21
CBO
Further analysis using survey measures of inflation expectations suggests:
 Inflation expectations by consumers matter more for inflation dynamics than the
expectations by professional forecasters for all ten measures of inflation
– Consumers’ expectations more closely resemble those of firms (Coibion and
Gorodnichenko, 2015)
– Transmission of professional forecasters’ views to consumers is weak in a low-
inflation environment
– Coibion et al. (2017): Similar finding for headline CPI
 Long-run inflation expectations by consumers are “shock-anchored” but not
“level-anchored” (Ball and Mazumder, 2011)
– Shock-anchoring: Transitory shocks not passed to expectations
– Level-anchoring: Expectations tied to a particular level
Estimation Results: I (Continued)

23. 22
CBO
 Comparing measures of core inflation
– The Phillips curve fits the non-XFE measures very well
 Average adj. 𝑅𝑅2
of non-XFE measures = 0.7
 Ball and Mazumder (2014): Showed this for median CPI
– XFEs are “outliers”, particularly XFE CPI-U (low 𝛼𝛼 and low 𝑅𝑅2)
 Average adj. 𝑅𝑅2 of XFE measures = 0.25
 Possible explanation
– Fewer goods prices in the non-XFE core measures
 Goods price changes are more volatile
 Goods price changes occur more frequently
Estimation Results: II

24. 23
CBO
CPI Components: Summary Statistics and Categorization
Mean
Standard
Deviation
Relative
Importance
(2017)
Change in
Relative
Importantce:
2007-2017
XFE Sticky CPI
Probability
(= Median CPI)
(1998-2007)
(1) (2) (3) (4) (5) (6) (7)
Core (XFE) Services
Owner's Equivalent of Rent (OER) 2.7 1.1 23.2% 2.98% Y Y 52%
Rent of Primary Residence 3.2 1.1 7.9% 1.01% Y Y 5%
Medical Care Services 3.8 1.3 6.7% 2.33% Y Y 2%
Education Services 4.9 1.5 3.0% 0.58% Y Y 0%
Transportation Services 2.7 1.8 6.0% -1.05% Y Y 5%
Core (XFE) Goods
Apparel -0.3 2.5 3.1% -1.89% Y N 2%
New Vehicles 0.1 2.3 3.6% -1.42% Y N 3%
Used Cars and Trucks -0.3 8 2.1% 0.20% Y N 0%
Medical Care Goods 2.9 1.6 1.8% 0.59% Y Y 1%
Food and Energy
Food away from Home 2.8 0.9 5.9% 0.19% N Y 11%
Food at Home 2.1 2.7 7.7% -2.01% N N 6%
Energy 3.6 20.2 7.5% 0.78% N N 1%
CategorizationSummary Statistics
Major CPI Components
The categorization of components into sticky CPI is based on Bryan and Meyer (2010), “Are Some Prices in the CPI More Forward Looking Than Others? We Think So,” Economic
Commentary, Federal Reserve Bank of Cleveland, https://www.frbatlanta.org/-/media/documents/research/inflationproject/stickyprice/sticky-price-cpi-supplemental-reading.pdf. The
probabilities of a component’s being the median CPI are based on the “revised methodology” that split the OER into four regional components. For more detail, see
https://www.clevelandfed.org/en/our-research/indicators-and-data/median-cpi/revised-methodology.aspx.

25. 24
CBO
 The slope of the Phillips curve: Flat, but steeper for CPIs than PCEPIs
– 𝛽𝛽 = 0.05∿0.1 for PCEPIs, but = 0.1∿0.2 for CPIs
– Why: Shelter, the most cyclically sensitive component, has a much larger weight in CPI than in PCEPI
Estimation Results: III
This figure plots the sum of the estimated coefficients on lagged inflation terms using recursive samples that start in 1998Q1 and end in 2012Q1, 2012Q2, …, and 2018Q1. The
Phillips curve equations are “unrestricted,” as no assumption was imposed on the value of π* before the estimation. Instead, the intercept of the equation, which, in theory, equals απ*,
was estimated and then the values of α and π* were calculated by assuming the long-run restriction on the estimated coefficients.

26. 25
CBO
 The slope of the Phillips curve: Flat, but steeper for CPIs than PCEPIs.
– 𝛽𝛽 = 0.05∿0.1 for PCEPIs, but = 0.1∿0.2 for CPIs
– Why: Shelter, the most cyclically sensitive component, has a much larger weight in CPI than in PCEPI.
Estimation Results: III (Continued)
This figure plots the sum of the estimated coefficients on lagged inflation terms using recursive samples that start in 1998Q1 and end in 2012Q1, 2012Q2, …, and 2018Q1. The
Phillips curve equations are “unrestricted,” as no assumption was imposed on the value of π* before the estimation. Instead, an intercept of the equation, which, in theory, equals απ*,
was estimated and then the value of α and π* were calculated by assuming the long-run restriction on the estimated coefficients.

27. 26
CBO
Reviewing the Findings

28. 27
CBO
 Phillips-curve analysis at the component level provides insight into:
– Cyclical sensitivity of aggregate inflation
 For most service components and food: inflation process is pro-cyclical
 For most non-food good components, inflation process is not pro-cyclical
 Need better understanding and models for goods price inflation
– Difference in the behaviors of various inflation measures
 CPI is more cyclically sensitive than PCEPI because shelter has larger share in
CPI
 Non-XFE measures of core inflation better capture movements in trend
inflation because they contain fewer noisy goods components
 The aggregate Phillips curve has shifted away from “accelerationist” toward an
“anchored” form, but the process appears incomplete
– Need better understanding of the formation process of inflation expectations,
particularly those of consumers and firms
Conclusions

29. 28
CBO
 Abdih, Yasser, Ravi Balakrishnan, and Baoping Shang. “What Is Keeping US Core
Inflation Low: Insights From a Bottom-Up Approach.” International Monetary Fund,
2016.
 Ball, Laurence, and Sandeep Mazumder. “Inflation Dynamics and the Great
Recession.” Brookings Papers on Economic Activity (2011): 337–406.
 Blanchard, Olivier. “The Phillips Curve: Back to the ’60s?" American Economic
Review 106.5 (2016): 31–34.
 Bils, Mark, and Peter J. Klenow. “Some Evidence on the Importance of Sticky
Prices.” Journal of Political Economy 112.5 (2004): 947–985.
 Coibion, Olivier, and Yuriy Gorodnichenko. “Is the Phillips Curve Alive and Well After All?
Inflation Expectations and the Missing Disinflation.” American Economic Journal:
Macroeconomics 7.1 (2015): 197–232.
References

30. 29
CBO
 Coibion, Olivier, Yuriy Gorodnichenko, and Rupal Kamdar. “The Formation of
Expectations, Inflation and the Phillips Curve.” No. w23304. National Bureau of
Economic Research, 2017.
 Goolsbee, Austan D., and Peter J. Klenow. “Internet Rising, Prices Falling: Measuring
Inflation in a World of E-Commerce.” AEA Papers and Proceedings. Vol. 108. 2018.
 Stock, J., and Mark Watson. “Slack and Cyclically Sensitive Inflation.” ECB Forum on
Central Banking, Sintra, Portugal. 2018.
 Struyven, Dann. “Which Prices Still Respond to Slack?” Goldman Sachs Economics
Research (October 31, 2017).
References (Continued)